Take a walk around the historical dam.
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Sculpture park founded by and with many sculptures by the British sculptor Tony Cragg, who lives and works in Wuppertal. Also has works by other modern and contemporary sculptors, and temporary exhibitions.
In a converted underground bunker, this club playing, amongst others, electronic music, is supposedly one of the clubs with the best acoustics (as to the Guardian)
A nice wide park on a hill in the heart of Wuppertal. On the park area there is also the Botanischer Garten (botanical garden).
the historical city hall
Nowadays the Stadthalle is a concert hall, host to many cultural events.
Museum for Early Industrialisation
Even though it costs money to get in (€4 for adults), it's worth a visit because they let one help operate one of the antique machines. The signs are only in German, so if you don't speak it, you might want to bring a native speaker or see ahead of time whether they have audio tours, or English speakers working at the museum.
Friedrich Engels is perhaps one of Barmen's most famous sons. He was not born in this house (the actual birth house some 100 metres away did not survive the war) but he did grow up here and his father was born here. While Trier has learned to make their native son Karl Marx into a tourism attraction, the co-founder of Marxism and Marx's long-time financier and best friend does not have the name recognition (it's not "Engelsism", after all) and Wuppertal has thus far failed to really market its connection to the son of a cotton manufacturer born in 1820.